"I watched in Jersey City, New Jersey - where thousands and thousands of people were cheering as the Towers came down,” he said at a rally in Birmingham, Alabama, over the weekend.

Trump repeated the claim on ABC’s This Week on Sunday.

“There were people that were cheering on the other side of New Jersey where you have large Arab populations,” he said. “They were cheering as the World Trade Center came down. I know it might be not politically correct for you to talk about it, but there were people cheering as that building came down -- as those buildings came down, and that tells you something. It was well covered at the time."

The citizens of Jersey City witnessed the tragedy of 9/11 from their own backyards. The Twin Towers loomed in the backdrop of the city. For 14 years an urban legend has persisted that some Muslims who live in Jersey City celebrated as the Towers fell. But that legend has long been discredited. The police and local politicians say it never happened.

Jersey City Mayor Steve Fulop responded to Trump’s claims and said he "has memory issues or willfully distorts the truth, either of which should be concerning for the Republican Party."